Lesson 24a - Absolute Conditional Convergence

# 1 n b n thismeansthattheabsoluteseriesconvergesby

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: test as: n 3 2n 1 n 2 an lim lim 5 n b n n 3n 2 2 1 n n 5 2n 3 n 2 an lim lim 5 n b n n 3n 2 2 n n 5 2n 3 n 2 5 5 5 an lim lim n 5 n 2 n n b n n 3n 2 n 5 5 5 n n n 2 1 1 2 3 a n lim n lim n n b n 3 2 n 1 3 5 n n a lim n 1 n b n This means that the absolute series converges by limit comparison test (1<infinity). This means the series is absolutely convergent. Example 2 Determine if the following series converges absolutely, conditionally, or diverges: n (1) n n2 e n Here we can see that the limit as n infinity produces: en en lim ( ) lim ( ) n n...
View Full Document

## This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

Ask a homework question - tutors are online